Parametric models may be generated by a computer for producing animated characters with deformable facial expressions. To simulate the complexity of muscle movement in a character's face, one or more modeling techniques may be implemented. For example, physically-based modeling techniques may be implemented that attempt to simulate various skin layers, muscles, tissues, bone and other components to approximate the mechanics of a face. In another technique, the character's face may be reduced to a collection of vertices whose positions may be adjusted to different facial expressions. Dependent upon the desired level of resolution, an extremely large number of vertices (e.g., tens of thousands, millions, etc.) may be included in such models. For some facial expressions, the positions of relatively few vertices may be adjusted, while significant position adjustments may be needed for representing other expressions.